A theorem on special linear groups

THE RATIONAL CHARACTER TABLE OF SPECIAL LINEAR GROUPS

In this paper we will give the character table of the irreducible rational representations of G=SL (2, q) where q= , p prime, n>O, by using the character table and the Schur indices of SL(2,q).

A splitting theorem for linear polycyclic groups

We prove that an arbitrary polycyclic by finite subgroup of GL(n,Q) is up to conjugation virtually contained in a direct product of a triangular arithmetic group and a finitely generated diagonal group.

A purity theorem for linear algebraic groups

Given a characteristic zero field k and a dominant morphism of affine algebraic k-groups μ : G → C one can form a functor from k-algebras to abelian groups R 7→ F(R) := C(R)/μ(G(R)). Assuming that C is commutative we prove that this functor satisfies a purity theorem for any regular local k-algebra. Few examples are considered in the very end of the preprint.

A Recognition Algorithm for Special Linear Groups

At the 1988 Oberwolfach Computational Group Theory meeting, Joachim Neubiiser asked for an efficient algorithm to decide whether the subgroup of the general linear group GL(d, q) generated by a given set X of non-singular d X d matrices over a finite field ¥q contains the special linear group SL(rf, q). Amplifying the problem he said he would be happy to have a program that could be used for ge...

On the Restriction of Characters of Special Linear Groups of Dimension Three